Theorems · Theorem · algebraic geometry

Algebra.smoothLocus_comap_of_isLocalization

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {Af : Type u_3}
  [inst_3 : CommRing Af] [inst_4 : Algebra A Af] [inst_5 : Algebra R Af] [IsScalarTower R A Af] (f : A)
  [IsLocalization.Away f Af],
  PrimeSpectrum.comap (algebraMap A Af) ⁻¹' Algebra.smoothLocus R A = Algebra.smoothLocus R Af

Defined in

Mathlib.RingTheory.Smooth.Locus

Cited by

1 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerIsLocalization.Away